In a steering system a steering wheel is typically coupled to a steering column, or shaft, in order for a driver to steer a vehicle. When the driver is travelling in essentially a straight-line path, the steering wheel is generally centered in a neutral position so as to have little effect on the path of travel. However, outside influences may require the steering wheel be rotated a small amount away from center in order to steer the vehicle substantially straight-ahead.
In cases where the steering wheel is pulled in one direction by outside influences, the driver must exert some force to prevent the vehicle from deviating from its intended straight-line path. This is commonly known as “steering pull” and can be caused by many outside influences such as road surface crown, tire properties, and vehicle front-end misalignment.
When a vehicle is driving on a road crown or road band, the side force on the vehicle due to the gravity force pushes the vehicle to one side. If the steering wheel is free to move, the vehicle will steer in the direction of the side force, denoted as F, in a circle such that the radius, denoted as R, is determined by the equation:
                              m          ⁢                                          ⁢                                    V              2                        R                          =        F                            (        1        )            
where V is the vehicle speed and m is the vehicle mass. The greater the side force, F, or the larger the road crown angle, the larger lateral drift of the vehicle and the smaller a turning radius.
To keep straight line driving, the vehicle lateral acceleration must be zero and either the vehicle yaw rate must be zero or the vehicle side slip must be constant. To meet these conditions, the forces and moments resulting from the side force, F, must be balanced by the forces and moments from the vehicle's tires so that a total lateral force, as well as a total yaw moment on the vehicle, are zero.
As discussed above, in a vehicle without automatic pull compensation, the driver must turn the steering wheel against the side force direction such that the front and rear tire forces and moments are developed thereby meeting the two necessary conditions.
Constant steering effort is necessary for driving straight-forward on a road with road-crown or road bank and increases driver fatigue over time. Existing steering pull compensation strategies use the driver's steering efforts as a reference to introduce a correction torque in the vehicle, in particular in a vehicle equipped with electric power assisted steering. This means the driver must first feel the torque before the torque can be compensated. Once a steering pull condition has been detected, there is a need for a control system in the vehicle to correct steering pull, in a short period of time or before the driver feels the effect of steering pull.